Sensor processing method

ABSTRACT

A pressure sensor and method wherein a resonant pressure transducer has a frequency F which changed depending on the applied pressure P and the temperature T. A temperature sensor measures the temperature T. A memory includes stored therein data points corresponding to the sensor&#39;s frequency F at difference applied pressures and temperatures. A processor is configured to generate several polynomials from the data points and calculate Pμ at Tμ when the transducer frequency is Fμ.

FIELD OF THE INVENTION

This subject invention relates to sensors, in one example, a pressuresensor.

BACKGROUND OF THE INVENTION

Sensors must be calibrated. In one example, a pressure indicatorincludes a resonant pressure transducer whose frequency changesdepending upon the applied pressure. The relationship between the sensorinput (pressure) and the sensor output (frequency changes) however, isnot linear. Moreover, the resonant frequency also changes as a functionof temperature. Thus, the pressure indicator typically includes atemperature sensor and both temperature and frequency signals are inputto a microprocessor. Calibration and compensation data is stored in amemory, (i.e., an EEPROM) linked to the microprocessor.

During calibration, several known pressures are applied to the sensor atseveral known temperatures. The microprocessor, programmed to applyvarious curve fitting techniques, then calculates the calibration dataand stores it in the memory in the form:P=ƒ(F,T)  (1)where F is the frequency, P is the pressure, and T is temperature. Inone example,

P = a₀ + b₀ ⋅ F + c₀ ⋅ F² + d₀ ⋅ F³ + a₁ ⋅ T + b₁ ⋅ F ⋅ T + c₁ ⋅ F² ⋅ T + d₁ ⋅ F³ ⋅ T + a₂ ⋅ T² + b₂ ⋅ F ⋅ T² + c₂ ⋅ F² ⋅ T² + d₂ ⋅ F³ ⋅ T² + a₂ ⋅ T³ + b₃ ⋅ F ⋅ T³ + c₃ ⋅ F² ⋅ T³ + d₃ ⋅ F³ ⋅ T³Here the coefficients a₀ . . . d₃, are calculated from the calibrationdata and are used to approximate the relation of F and T to the outputP. Linear approximation schemes such as least square fit, or an exactfit from a prescribed number of data points may be used.

When the sensor is used in the field, the microprocessor notes thetemperature and frequency of the transducer and calculates the pressurereadout based on equation (2).

For high accuracy use, this scheme has a number of limitations.

First, the fit of the polynomial is dependent on the order of thepolynomial chosen. Higher order polynomials provide a better fit butsignificantly increase the computational burden which limits the speedand accuracy of calculations.

Second, high order polynomials are notoriously ill behaved and exhibitoscillatory characteristics not fount in the original data.

Third, the estimation at the boundaries of the original data is poor,with extreme divergence outside of the boundaries of the original data.

Other methods such as Bezier curves and Hermite Splines may also be usedto overcome some of the unnatural behaviors of the polynomials. Suchmethods, however, involve significant computational burden thus limitingtheir usefulness in systems where computational power is limited.

Cubic splines techniques have also been used to fit data. Such methodshave the advantage that curvature is controlled to avoid sharptransitions. However, such methods depend on prior knowledge ofcurvature constraints and end point characteristics that are oftenunknown or too variable creating errors in the resultant fit that do notappear in the measurement data. Furthermore, the complexity of thecalculation is substantial.

In the prior art, the calculations involved require the use of doubleprecision floating point operations to maintain calculation errors below1 ppm. This alone almost quadruples the computational load for a smallmicroprocessor based system.

BRIEF SUMMARY OF THE INVENTION

The subject invention features a new processing method for a pressuresensor. The pressure and temperature effects of a sensor are correctedusing calibration points and highly efficient and accurate algorithms.The method allows rapid and accurate determinations of the output of asensor and avoids the need for double precision floating pointcalculations. The method minimizes rounding errors, results in fastersignal processing, and results in lower power consumption. The subjectinvention further features a pressure sensor which incorporates themethod discussed above. Moreover, the method can be employed with othertypes of sensors.

In one aspect, the subject invention features a method of sensingpressure. The method comprises subjecting a pressure sensor having anoutput P which varies based on the sensor's frequency F and thetemperature T to several different temperatures and applied pressures,determining the sensor's frequency F at the different temperatures andapplied pressures and collecting data points representing the same, and,from the data points and at each different temperature, generatingseveral polynomials P=ƒ(F) and T=ƒ(F). The sensor is then used to sensean unknown pressure Pμ at a temperature Tμ at which the sensor has afrequency Fμ. From the generated polynomials, several polynomials thatsurround Tμ and Fμ are selected. Those polynomials are evaluated for Fμto calculated values for P=ƒ(Fμ) and T=ƒ(Fμ). From the calculatedvalues, a polynomial P=ƒ(T) is generated and solved for Tμ in order tooutput Pμ.

In one example, generating the polynomials includes employing Newton'smethod. The generated polynomials may be stored or the data points canbe stored and then the polynomials are not generated until thesurrounding data points are selected. Solving Pμ=ƒ(T) may include usingLagrange's method.

The subject invention also features a pressure sensor comprising aresonant pressure transducer whose frequency F changes depending on theapplied pressure P and the temperature T, a temperature sensor formeasuring the temperature T, and a memory including stored therein datapoints corresponding to the sensor's frequency F at different appliedpressures and temperatures. A processor is configured to generateseveral polynomials P=ƒ(F) and T=ƒ(F) from the data points and tocalculate Pμ at Tμ when the transducer frequency is Fμ. From thegenerated polynomials, polynomials that surround Fμ and Tμ are selected,the selected polynomials are evaluated for Fμ to calculated values forP=ƒ(Fμ) and T=ƒ(Fμ), a polynomial P=ƒ(T) is generated for the calculatedvalues and Pμ=ƒ(T) is solved for Tμ. The processor then outputs Pμ.

More generically, the subject invention features a method of determiningan unknown parameter Z based on two measured parameters X and Y. Thepreferred method comprises determining Z at different values of X and Yand collecting data points representing the same. From the data points,several polynomials Z=ƒ(X) and X=ƒ(Y) are generated. An unknownparameter Zμ at Xμ and Yμ is determined. From the generated polynomials,polynomials that surround Xμ and Yμ are selected. The selectedpolynomials are evaluated for Yμ to calculated values for Z=ƒ(Yμ) andX=ƒ(Yμ). From the calculated values, a polynomial X=ƒ(X) is generated.Zμ=ƒ(X) for Xμ is solved and Zμ is output.

A sensor system is accordance with the subject invention features asensor with a parameter Y that changes depending on parameter Z andparameter X. A device measures parameter X. A memory includes storedtherein data points corresponding to values of parameter Y at differentvalues of Z and Z. A processor is configured to general severalpolynomials from the data points and calculated Zμ at Xμ when the sensormeasure Yμ. Polynomials that surround Yμ and Xμ are selected andevaluated for Yμ to calculated values for Z=ƒ(Yμ) and X=ƒ(Yμ). Apolynomial Z=ƒ(X) is generated for the calculated values, and Zμ=ƒ(X) issolved for Xμ.

The subject invention, however, in other embodiments, need not achieveall these objectives and the claims hereof should not be limited tostructures or methods capable of achieving these objectives.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

Other objects, features and advantages will occur to those skilled inthe art from the following description of a preferred embodiment and theaccompanying drawings, in which:

FIG. 1 shows an example of calibration data points collected inaccordance with the subject invention;

FIG. 2 depicts how a polynomial is calculated in accordance with thesubject invention;

FIG. 3 shows how six points create three cubic polynomials from fouradjacent data points in accordance with the subject invention;

FIG. 4 shows how the most accurate estimation is in the region boundedby the two centermost points that created the polynomial;

FIG. 5 shows how four surrounding sets provide four valves of pressureand four valves of temperature in accordance with the subject invention;and

FIG. 6 is a highly schematic block diagram showing the primarycomponents associated with an example of a sensor in accordance with thesubject invention.

DETAILED DESCRIPTION OF THE INVENTION

Aside from the preferred embodiment or embodiments disclosed below, thisinvention is capable of other embodiments and of being practiced orbeing carried out in various ways. Thus, it is to be understood that theinvention is not limited in its application to the details ofconstruction and the arrangements of components set forth in thefollowing description or illustrated in the drawings. If only oneembodiment is described herein, the claims hereof are not to be limitedto that embodiment. Moreover, the claims hereof are not to be readrestrictively unless there is clear and convincing evidence manifestinga certain exclusion, restriction, or disclaimer.

The subject invention uses simple interpolating polynomial functionsthat represents the function accurately over a narrow range in onedimension. The full range is achieved by providing sets of suchpolynomials. Two dimensional interpolation is then realized by creatingseveral sets of polynomials which are then combined to form a unifiedrepresentation of the data.

Typically, calibration data points are collected from measurements takento form grid of sensor characteristics in at least two variables. In oneexample, this would be the measurement of sensor frequency F and sensortemperature T at various applied pressures (P_(applied)) and testtemperatures (T_(applied)). For example, this might be at 9 pressuresand 5 temperatures yielding 45 data points as shown in FIG. 1. There isno requirement for the grid to be either equally spaced nor containequal number of points in each dimension. Indeed, it may be preferableto have a higher point density in areas of uncertainty.

Each of these points would have associated with them precisely measuredvalues of P, F and T. The measured values of P and T may differsignificantly from the applied values.

Various means are used to fit an interpolating polynomial of order “n”to “n+1” data points. This solution is unique and the function exactlypasses thru the calibration data points. For example, 4 points can beused to define the cubic polynomial shown in FIG. 2.

For each row in the point grid or FIG. 1, there are a set of pointsrepresenting the function. Several “n^(th)” order polynomials can befitted to adjacent data points. If the number of points in the row is P,there will be p-n such polynomials.

In this example, each value of T_(applied) will have 9 points (P, F, T)allowing a set of six cubic polynomial P=ƒ(F) to be calculated for eachvalue of T_(applied).

FIG. 3 shows how 6 points create 3 cubic polynomials from 4 adjacentpoints.

Since the polynomials overlap, they provide several estimates of thefunction. The most accurate estimation is in the region bounded by thetwo centermost points that created the polynomial as shown in FIG. 4. Atthe extremes of data, where no choice exists we use the nearestpolynomial estimation can be used.

With this selection, there is now a method to provide an accurateestimation across the range bounded by the data points. There will beone such estimate for every row in the original data.

The process is then repeated for the second variable. In the example,this would yield 6 polynomials T=ƒ(F) for each value of T_(applied). Thetwo polynomial sets above are created for all rows. So in the presentexample, this would give 5 sets, each containing 6 polynomials P=ƒ(F)and 6 polynomials T=ƒ(F).

Calculation of these all polynomials (60 in this example) may present asevere challenge to both the computational power and accuracy that canbe achieved in a simple sensor device. So, Newton's method can be usedto solve these polynomials. This method accurately computes theNewtonian form of polynomial and can exploit the adjacent nature of thepoints to use “Newton's Triangle” to substantial reduce computationalrequirements and enhance accuracy.

The polynomials may be pre-calculated and held in memory. Alternativelythe defining data points alone may be held in memory and polynomialcalculation delayed until it is needed. For the first method, there aretwo tables of 30 polynomials related to the row/column order of theoriginal data points (instead of 9×5, there would be 6×5 i.e. 5 setseach containing 6 polynomials.)

In the field where the pressure sensor is subjected to a pressure P at atemperature Tμ, the frequency of the transducer is Fμ. To evaluate thefunction P at any point FμTμ, the polynomial sets that surround thepoint are selected. Selection of these polynomials (or their definingpoints) is accomplished using a simple search of the data point tableheld in memory. For the unknowns Tμ and Fμ, the table of polynomials issearched to find the ones which surround the unknown. In the example,four are needed for a cubic fit so that is two on either side. For thesecond method, only the original data is stored. So, instead of findingthe four polynomials which surround Tμ and Fμ, all the points whichdefine those polynomials are located. This would be a collection of 16points that surround Tμ and Fμ. A cubic function suits the variabilityof P with T, so for any given point the four nearest sets that surroundthat point are selected.

Each of these sets of polynomials can now be evaluated to give P and Tvalues for the given value of Fμ using a substitution in thepre-calculated Newtonian polynomials. Alternatively a combinedinterpolation and evaluation of the original data points usingLagrange's method can be employed. In this case, 16 original data pointswould be chosen, to create four polynomials.

In our example, the four surrounding sets provide four values of P andfour values of T for the given value Fμ as shown in FIG. 5.

These four new points define a cubic polynomial function P=ƒ(T) whichcan then be evaluated at the given value of Tμ to provide final outputP.

As only one evaluation is needed for the final polynomial, it isadvantageous to use Lagrange's method to combine both interpolation andevaluation operations. This has lower computational demands and higheraccuracy than separately creating the polynomial and evaluating it.

As has been shown, Lagrange and Newton's method can be used tosubstantially reduce the computational power required. Newton's methodallows a pre-calculation of all the polynomials in an accurate andefficient manner leaving only the evaluation of m+1 of these polynomialsand final interpolation using Lagrange's method.

Alternatively, to conserve memory, just the original data points maybebe stored. Lagrange's method can then be used to combine bothinterpolation and evaluation.

FIG. 6 shows pressure sensor 10 having an output P and transducer 12which generates a different frequency F when subject to differentpressures. Temperature sensor 14 measures the temperature T. Processor16 is responsive to both F and T and is configured (e.g.) programmed tooperate according to the method discussed above. EEPROM 18 (or someother memory) stores the values of F and P at different temperatures Tas discussed above in reference to FIG. 1. Processor 16 outputs (to adisplay, for example) Pμ when transducer 12 is subject to Pμ attemperature Tμ and exhibits a frequency Fμ. The above method has yieldedaccuracy of better than 1 ppm using single precision floating pointcalculations.

But, the subject invention is not limited to pressure transducers andthe method described above can be used with other types of sensors.Generally, it is assumed that data has been collected from test orcalibration measurements. This data is of the form (X,Y,Z). For example,consider a test of a pressure sensor across a range of different appliedpressures and temperatures. Z is the measured pressure, X is thetemperature sensor measurement and Y is the output of the sensor.

The following procedure will then accurately estimate the value of Z forany given value of X=x and Y=y, using a two dimensional polynomialfunction of order m×n.

In step one, the data points (X,Y,Z) are arranged to represent a grid ofZ values for two input variables X and Y where X and Y are in monotonicorder. See FIG. 1. In step two, the (m+1) by (n+1) point matrix thatspans the (x, y) point to be evaluated is selected. In step three, m+1polynomials of order n using n+1 points where Z=J(Y) are solved. In stepfour, m+1 polynomials of order n using n+1 points where X=J(Y) aresolved. In step five, the polynomials found in step four, are evaluatedfor the input value of Y=y to give m+1 values for Z and X. In step six,the polynomial of order m is solved using the m+1 data points forZ=ƒ(X). Then, in step seven, Z is evaluated using the polynomial fromstep six for the input value of X=x.

Selecting the point matrix may be accomplished using a search of thedata values. This search maybe optimized for efficiency usingestablished methods.

Steps three and four, solving the Z=ƒ(Y) and X=ƒ(Y) polynomials, may beoptimized by pre-calculating the polynomials using the Newtonian form topreserve accuracy and calculation efficiency. Alternatively, these stepsand the evaluation step may be combined using Lagrange's interpolationto reduce memory requirements and still maintains accuracy. The last twosteps are preferably combined using Lagrange's interpolation andevaluation.

The subject invention can be employed in a wide variety of sensor andcontrol applications. For example, in engine control, it is common totake two measurements to derive a third parameter. For example, RPM andmanifold pressure can be used to determine ignition timing. The methodof this invention can be used in such an application and the originaldata might be based on experimental or modeled conditions and the outputwould not typically be an indicator but instead part of the overallsystem control function.

Thus, although specific features of the invention are shown in somedrawings and not in others, this is for convenience only as each featuremay be combined with any or all of the other features in accordance withthe invention. The words “including”, “comprising”, “having”, and “with”as used herein are to be interpreted broadly and comprehensively and arenot limited to any physical interconnection. Moreover, any embodimentsdisclosed in the subject application are not to be taken as the onlypossible embodiments. Other embodiments will occur to those skilled inthe art and are within the following claims.

In addition, any amendment presented during the prosecution of thepatent application for this patent is not a disclaimer of any claimelement presented in the application as filed: those skilled in the artcannot reasonably be expected to draft a claim that would literallyencompass all possible equivalents, many equivalents will beunforeseeable at the time of the amendment and are beyond a fairinterpretation of what is to be surrendered (if anything), the rationaleunderlying the amendment may bear no more than a tangential relation tomany equivalents, and/or there are many other reasons the applicant cannot be expected to describe certain insubstantial substitutes for anyclaim element amended.

1. A method of sensing pressure with a pressure sensor, the methodcomprising: subjecting the pressure sensor having on output P whichvaries based on the sensor's frequency F and the temperature T toseveral different temperatures and applied pressures; determining thepressure sensor's frequency F at the different temperatures and appliedpressures and collecting data points representing the same; from thedata points and at each different temperature, generating severalpolynomials P=ƒ(F) and T=ƒ/(F); using the pressure sensor to sense anunknown pressure Pμ at a temperature Tμ at which the pressure sensor hasa frequency Fμ; selecting, from the generated polynomials, polynomialsthat surround Tμ and Fμ; evaluating the selected polynomials for Fμ tocalculate values for P=ƒ(Fμ) and T=ƒ(Fμ); from the calculated values,generating a polynomial P=ƒ(T); and solving Pμ=ƒ(T) for Tμ andoutputting Pμ.
 2. The method of claim 1 in which generating thepolynomials includes employing Newton's method.
 3. The method of claim 1in which the generated polynomials are stored.
 4. The method of claim 1in which the data points are stored and the polynomials are notgenerated until the surrounding data points are selected.
 5. The methodof claim 1 in which solving Pμ=ƒ(T) includes using Lagrange's method. 6.A pressure sensor comprising: a resonant pressure transducer whosefrequency F changes depending on the applied pressure P and thetemperature T; a temperature sensor for measuring the temperature T; amemory including stored therein data points corresponding to thesensor's frequency F at different applied pressures and temperatures;and a processor configured to: generate several polynomials P=ƒ/(F) andT=ƒ(F) from the data points, calculate Pμ at Tμ when the transducerfrequency is Fμ by: selecting, from the generated polynomials,polynomials that surround Fμ and Tμ, evaluating the selected polynomialsfor Fμ to calculate values for P=ƒ(Fμ) and T=ƒ(Fμ), generating apolynomial P=ƒ(T) for the calculated values, and solving Pμ=ƒ(T) for Tμ,and output Pμ.
 7. A method of determining an unknown parameter Z basedon two parameters X and Y measured at least a first sensor, the methodcomprising: determining Z with a second sensor at different values of Xand Y and collecting data points representing the same; from the datapoints, generating several polynomials Z=ƒ(X) and X=ƒ(Y); determining anunknown parameter Zμ at Xμ and Yμ; selecting, from the generatedpolynomials, polynomials that surround Xμ and Yμ; evaluating theselected polynomials for Yμ to calculate values for Z=ƒ(Yμ) and X=ƒ(Yμ);from the calculated values, generating a polynomial Z=ƒ(X); and solvingZμ=ƒ(X) for Xμ and outputting Zμ.
 8. The method of claim 7 in whichgenerating the polynomials includes employing Newton's method.
 9. Themethod of claim 7 in which the generated polynomials are stored.
 10. Themethod of claim 7 in which the data points are stored and thepolynomials are not generated until surrounding data points areselected.
 11. The method of claim 7 in which solving Zμ=ƒ(X) includesusing Lagrange's method.
 12. A sensor system comprising: a sensor with aparameter Y that changes depending on parameter Z and parameter X; adevice which measures parameter X; a memory including stored thereindata points corresponding to values of parameter Y at different valuesof Z and X; and a processor configured to: generate several polynomialsZ=ƒ(X) and X=ƒ(Y) from the data points, calculate Zμ at Xμ when thesensor measures Yμ by: selecting, from the generated polynomials,polynomials that surround Yμ and Xμ, evaluating the selected polynomialsfor Yμ to calculate values for Z=ƒ(Yμ) and X=ƒ(Yμ), generating apolynomial Z=ƒ(X) for the calculated values, and solving Zμ=ƒ(X) for Xμ,and output Zμ.